Fast uncertainty quantification of tracer distribution in the brain
interstitial fluid with multilevel and quasi Monte Carlo

Efficient uncertainty quantification algorithms are key to
understand the propagation of uncertainty -- from uncertain input
parameters to uncertain output quantities -- in high resolution
mathematical models of brain physiology. Advanced Monte Carlo
methods such as quasi Monte Carlo (QMC) and multilevel Monte Carlo
(MLMC) have the potential to dramatically improve upon standard
Monte Carlo (MC) methods, but their applicability and performance in
biomedical applications is underexplored. In this paper, we design
and apply QMC and MLMC methods to quantify uncertainty in a
convection-diffusion model of tracer transport within the brain. We
show that QMC outperforms standard MC simulations when the number of
random inputs is small. MLMC considerably outperforms both QMC and
standard MC methods and should therefore be preferred for brain
transport models.